A What if i do not go into orbit but close in on a langrange p

so imagine a rocket with module is not going into orbit but just, after loss of stages, continues to a lagrange point. At what distance, before reaching the actual point, could the module with some leftover fuel and maybe solar power or wind stay there, let us say for some months, before new supplies, propellant, are brought to keep it there, hence, maybe expanding it to a new kind of ISS ? Or is this just totally unfeasible and is it better to actually go all the way to the point? Even then, these points can be unstable and modules would also need fuel to stay put.

Excuse my ignorance, but doesn't it take significantly more energy to get to any of the L points than orbit? I don't think the solar wind would help much at that altitude either, the earths magnetosphere is still pretty overwhelming at that distance.

Getting from low earth orbit to any lagrangian requires going faster than escape velocity and the nearest one is around the orbit of the moon around Earth so all of them are about 400,000 kilometers away from Earth. If you were short of those points you would continue on whatever orbit you would have going around Earth, in a big elliptical orbit. It would depend on exactly what your orbit is to keep from crashing back to Earth. Reaching escape velocity means you never get back to Earth but I think you could still crash by getting too close to Earth on the downwards trip, skimming above Earth low enough to be dragged down by the atmosphere and at that point you better hope your heat shields hold up and your parachutes deploy if you don't want to first be just glowing debris and second, passing that problem, not hitting the ground or ocean doing 500 km/hr which would definitely ruin your day....

NewJersey runner, Earth's magnetic field can extend past the moon but only in some directions so it would be a crap shoot if you were in that field or not. You could still be hit by active solar winds and that would ruin your day also.

Thanks allready for your reactions. So i understand a direct ascend to, let's say moon L1 is crazy because it consumes way more fuel than going into orbit around earth and then slowly ascend to the L1 point. But,then again, once you are on the point and you want to stay there you have to match the orbital speed of the moon that is way slower, and thus descelerate again. But still this is the most efficient way with current technology to get there, right ? As i read somewhere some satellites got there and could stay there for some time but i do not know how they did it and certainly not how much energy was still needed to keep them there because those points can still be unstable at times. If it turns out not much energy is needed then maybe it can be harvested from solar power only ( panels, sails). For a future station there that could be important.